Improving Spatial Domain Repetition of Implicit Surfaces

Implicit surfaces offer distinct advantages over traditional boundary representations, including infinite resolution, low memory footprint, smooth geometry by construction, and support for non-destructive modeling. In this work, we introduce a method for localizing geometric detail in a way that preserves the mathematical properties required for accurate and efficient rendering using sphere tracing. Our contributions include novel procedural modeling techniques that expand the range of repetition patterns achievable in implicit surfaces; an interpolation-based approach that maintains field correctness while remaining computationally efficient; and a cache-based acceleration strategy that significantly improves the rendering performance of domain-repeated implicit geometries.